HomeAdam: Adam and AdamW Algorithms Sometimes Go Home to Obtain Better Provable Generalization

Adam and AdamW are a class of default optimizers for training deep learning models in machine learning. These adaptive algorithms converge faster but generalize worse compared to SGD. In fact, their proved generalization error $O(\frac{1}{\sqrt{N}})$ also is larger than $O(\frac{1}{N})$ of SGD, where $N$ denotes training sample size. Recently, although some variants of Adam have been proposed to improve its generalization, their improved generalizations are still unexplored in theory. To fill this gap, in the paper, we restudy generalization of Adam and AdamW via algorithmic stability, and first prove that Adam and AdamW without square-root (i.e., Adam(W)-srf) have a generalization error $O(\frac{\hatρ^{-2T}}{N})$, where $T$ denotes iteration number and $\hatρ>0$ denotes the smallest element of second-order momentum plus a small positive number. To improve generalization, we propose a class of efficient clever Adam (i.e., HomeAdam(W)) algorithms via sometimes returning momentum-based SGD. Moreover, we prove that our HomeAdam(W) have a smaller generalization error $O(\frac{1}{N})$ than $O(\frac{\hatρ^{-2T}}{N})$ of Adam(W)-srf, since $\hatρ$ is generally very small. In particular, it is also smaller than the existing $O(\frac{1}{\sqrt{N}})$ of Adam(W). Meanwhile, we prove our HomeAdam(W) have a faster convergence rate of $O(\frac{1}{T^{1/4}})$ than $O(\frac{\breveρ^{-1}}{T^{1/4}})$ of the Adam(W)-srf, where $\breveρ\leq\hatρ$ also is very small. Extensive numerical experiments demonstrate efficiency of our HomeAdam(W) algorithms.

Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis

Atmospheric turbulence significantly degrades long-range imaging by introducing geometric warping and exposure-time-dependent blur, which adversely affects both visual quality and the performance of high-level vision tasks. Existing methods for synthesizing turbulence effects often oversimplify the relationship between blur and exposure-time, typically assuming fixed or binary exposure settings. This leads to unrealistic synthetic data and limited generalization capability of trained models. To address this gap, we revisit the modulation transfer function (MTF) formulation and propose a novel Exposure-Time-dependent MTF (ET-MTF) that models blur as a continuous function of exposure-time. For blur synthesis, we derive a tilt-invariant point spread function (PSF) from the ET-MTF, which, when integrated with a spatially varying blur-width field, provides a comprehensive and physically accurate characterization of turbulence-induced blur. Building on this synthesis pipeline, we construct ET-Turb, a large-scale synthetic turbulence dataset that explicitly incorporates continuous exposure-time modeling across diverse optical and atmospheric conditions. The dataset comprises 5,083 videos (2,005,835 frames), partitioned into 3,988 training and 1,095 test videos. Extensive experiments demonstrate that models trained on ET-Turb produce more realistic restorations and achieve superior generalization on real-world turbulence data compared to those trained on other datasets. The dataset is publicly available at: github.com/Jun-Wei-Zeng/ET-Turb.

Negatives-Dominant Contrastive Learning for Generalization in Imbalanced Domains

Imbalanced Domain Generalization (IDG) focuses on mitigating both domain and label shifts, both of which fundamentally shape the model's decision boundaries, particularly under heterogeneous long-tailed distributions across domains. Despite its practical significance, it remains underexplored, primarily due to the technical complexity of handling their entanglement and the paucity of theoretical foundations. In this paper, we begin by theoretically establishing the generalization bound for IDG, highlighting the role of posterior discrepancy and decision margin. This bound motivates us to focus on directly steering decision boundaries, marking a clear departure from existing methods. Subsequently, we technically propose a novel Negative-Dominant Contrastive Learning (NDCL) for IDG to enhance discriminability while enforce posterior consistency across domains. Specifically, inter-class decision-boundary separation is enhanced by placing greater emphasis on negatives as the primary signal in our contrastive learning, naturally amplifying gradient signals for minority classes to avoid the decision boundary being biased toward majority classes. Meanwhile, intra-class compactness is encouraged through a re-weighted cross-entropy strategy, and posterior consistency across domains is enforced through a prediction-central alignment strategy. Finally, rigorous yet challenging experiments on benchmarks validate the effectiveness of our NDCL. The code is available at https://github.com/Alrash/NDCL.

Beyond Observations: Reconstruction Error-Guided Irregularly Sampled Time Series Representation Learning

Irregularly sampled time series (ISTS), characterized by non-uniform time intervals with natural missingness, are prevalent in real-world applications. Existing approaches for ISTS modeling primarily rely on observed values to impute unobserved ones or infer latent dynamics. However, these methods overlook a critical source of learning signal: the reconstruction error inherently produced during model training. Such error implicitly reflects how well a model captures the underlying data structure and can serve as an informative proxy for unobserved values. To exploit this insight, we propose iTimER, a simple yet effective self-supervised pre-training framework for ISTS representation learning. iTimER models the distribution of reconstruction errors over observed values and generates pseudo-observations for unobserved timestamps through a mixup strategy between sampled errors and the last available observations. This transforms unobserved timestamps into noise-aware training targets, enabling meaningful reconstruction signals. A Wasserstein metric aligns reconstruction error distributions between observed and pseudo-observed regions, while a contrastive learning objective enhances the discriminability of learned representations. Extensive experiments on classification, interpolation, and forecasting tasks demonstrate that iTimER consistently outperforms state-of-the-art methods under the ISTS setting.

LiMuon: Light and Fast Muon Optimizer for Large Models

Large models recently are widely applied in artificial intelligence, so efficient training of large models has received widespread attention. More recently, a useful Muon optimizer is specifically designed for matrix-structured parameters of large models. Although some works have begun to studying Muon optimizer, the existing Muon and its variants still suffer from high sample complexity or high memory for large models. To fill this gap, we propose a light and fast Muon (LiMuon) optimizer for training large models, which builds on the momentum-based variance reduced technique and randomized Singular Value Decomposition (SVD). Our LiMuon optimizer has a lower memory than the current Muon and its variants. Moreover, we prove that our LiMuon has a lower sample complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of non-convex stochastic optimization under the smooth condition. Recently, the existing convergence analysis of Muon optimizer mainly relies on the strict Lipschitz smooth assumption, while some artificial intelligence tasks such as training large language models (LLMs) do not satisfy this condition. We also proved that our LiMuon optimizer has a sample complexity of $O(\epsilon^{-3})$ under the generalized smooth condition. Numerical experimental results on training DistilGPT2 and ViT models verify efficiency of our LiMuon optimizer.

Global Pre-fixing, Local Adjusting: A Simple yet Effective Contrastive Strategy for Continual Learning

Continual learning (CL) involves acquiring and accumulating knowledge from evolving tasks while alleviating catastrophic forgetting. Recently, leveraging contrastive loss to construct more transferable and less forgetful representations has been a promising direction in CL. Despite advancements, their performance is still limited due to confusion arising from both inter-task and intra-task features. To address the problem, we propose a simple yet effective contrastive strategy named \textbf{G}lobal \textbf{P}re-fixing, \textbf{L}ocal \textbf{A}djusting for \textbf{S}upervised \textbf{C}ontrastive learning (GPLASC). Specifically, to avoid task-level confusion, we divide the entire unit hypersphere of representations into non-overlapping regions, with the centers of the regions forming an inter-task pre-fixed \textbf{E}quiangular \textbf{T}ight \textbf{F}rame (ETF). Meanwhile, for individual tasks, our method helps regulate the feature structure and form intra-task adjustable ETFs within their respective allocated regions. As a result, our method \textit{simultaneously} ensures discriminative feature structures both between tasks and within tasks and can be seamlessly integrated into any existing contrastive continual learning framework. Extensive experiments validate its effectiveness.

Cut out and Replay: A Simple yet Versatile Strategy for Multi-Label Online Continual Learning

Multi-Label Online Continual Learning (MOCL) requires models to learn continuously from endless multi-label data streams, facing complex challenges including persistent catastrophic forgetting, potential missing labels, and uncontrollable imbalanced class distributions. While existing MOCL methods attempt to address these challenges through various techniques, \textit{they all overlook label-specific region identifying and feature learning} - a fundamental solution rooted in multi-label learning but challenging to achieve in the online setting with incremental and partial supervision. To this end, we first leverage the inherent structural information of input data to evaluate and verify the innate localization capability of different pre-trained models. Then, we propose CUTER (CUT-out-and-Experience-Replay), a simple yet versatile strategy that provides fine-grained supervision signals by further identifying, strengthening and cutting out label-specific regions for efficient experience replay. It not only enables models to simultaneously address catastrophic forgetting, missing labels, and class imbalance challenges, but also serves as an orthogonal solution that seamlessly integrates with existing approaches. Extensive experiments on multiple multi-label image benchmarks demonstrate the superiority of our proposed method. The code is available at \href{https://github.com/wxr99/Cut-Replay}{https://github.com/wxr99/Cut-Replay}

LoD: Loss-difference OOD Detection by Intentionally Label-Noisifying Unlabeled Wild Data

Using unlabeled wild data containing both in-distribution (ID) and out-of-distribution (OOD) data to improve the safety and reliability of models has recently received increasing attention. Existing methods either design customized losses for labeled ID and unlabeled wild data then perform joint optimization, or first filter out OOD data from the latter then learn an OOD detector. While achieving varying degrees of success, two potential issues remain: (i) Labeled ID data typically dominates the learning of models, inevitably making models tend to fit OOD data as IDs; (ii) The selection of thresholds for identifying OOD data in unlabeled wild data usually faces dilemma due to the unavailability of pure OOD samples. To address these issues, we propose a novel loss-difference OOD detection framework (LoD) by \textit{intentionally label-noisifying} unlabeled wild data. Such operations not only enable labeled ID data and OOD data in unlabeled wild data to jointly dominate the models' learning but also ensure the distinguishability of the losses between ID and OOD samples in unlabeled wild data, allowing the classic clustering technique (e.g., K-means) to filter these OOD samples without requiring thresholds any longer. We also provide theoretical foundation for LoD's viability, and extensive experiments verify its superiority.

ULFine: Unbiased Lightweight Fine-tuning for Foundation-Model-Assisted Long-Tailed Semi-Supervised Learning

Based on the success of large-scale visual foundation models like CLIP in various downstream tasks, this paper initially attempts to explore their impact on Long-Tailed Semi-Supervised Learning (LTSSL) by employing the foundation model with three strategies: Linear Probing (LP), Lightweight Fine-Tuning (LFT), and Full Fine-Tuning (FFT). Our analysis presents the following insights: i) Compared to LTSSL algorithms trained from scratch, FFT results in a decline in model performance, whereas LP and LFT, although boosting overall model performance, exhibit negligible benefits to tail classes. ii) LP produces numerous false pseudo-labels due to \textit{underlearned} training data, while LFT can reduce the number of these false labels but becomes overconfident about them owing to \textit{biased fitting} training data. This exacerbates the pseudo-labeled and classifier biases inherent in LTSSL, limiting performance improvement in the tail classes. With these insights, we propose a Unbiased Lightweight Fine-tuning strategy, \textbf{ULFine}, which mitigates the overconfidence via confidence-aware adaptive fitting of textual prototypes and counteracts the pseudo-labeled and classifier biases via complementary fusion of dual logits. Extensive experiments demonstrate that ULFine markedly decreases training costs by over ten times and substantially increases prediction accuracies compared to state-of-the-art methods.

Recent Advances in Out-of-Distribution Detection with CLIP-Like Models: A Survey

Out-of-distribution detection (OOD) is a pivotal task for real-world applications that trains models to identify samples that are distributionally different from the in-distribution (ID) data during testing. Recent advances in AI, particularly Vision-Language Models (VLMs) like CLIP, have revolutionized OOD detection by shifting from traditional unimodal image detectors to multimodal image-text detectors. This shift has inspired extensive research; however, existing categorization schemes (e.g., few- or zero-shot types) still rely solely on the availability of ID images, adhering to a unimodal paradigm. To better align with CLIP's cross-modal nature, we propose a new categorization framework rooted in both image and text modalities. Specifically, we categorize existing methods based on how visual and textual information of OOD data is utilized within image + text modalities, and further divide them into four groups: OOD Images (i.e., outliers) Seen or Unseen, and OOD Texts (i.e., learnable vectors or class names) Known or Unknown, across two training strategies (i.e., train-free or training-required). More importantly, we discuss open problems in CLIP-like OOD detection and highlight promising directions for future research, including cross-domain integration, practical applications, and theoretical understanding.