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Theory · Learning Theory

Itai Morad, Nir Shlezinger, Yonina Eldar

Knowledge Distillation (KD) is a central paradigm for transferring knowledge from a large teacher network to a typically smaller student model, often by leveraging soft probabilistic outputs. While KD has shown strong empirical success in numerous applications, its theoretical underpinnings remain only partially understood. In this work, we adopt a Bayesian perspective on KD to rigorously analyze the convergence behavior of students trained with Stochastic Gradient Descent (SGD). We study two regimes: $(i)$ when the teacher provides the exact Bayes Class Probabilities (BCPs); and $(ii)$ supervision with noisy approximations of the BCPs. Our analysis shows that learning from BCPs yields variance reduction and removes neighborhood terms in the convergence bounds compared to one-hot supervision. We further characterize how the level of noise affects generalization and accuracy. Motivated by these insights, we advocate the use of Bayesian deep learning models, which typically provide improved estimates of the BCPs, as teachers in KD. Consistent with our analysis, we experimentally demonstrate that students distilled from Bayesian teachers not only achieve higher accuracies (up to +4.27\%), but also exhibit more stable convergence (up to 30\% less noise), compared to students distilled from deterministic teachers.

Optimization · Sampling and Optimization

Yesom Park, Shu Liu, Mo Zhou, Stanley J Osher

We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By leveraging the method of characteristics, we derive closed-form, bidirectional transport maps, thereby eliminating the need for numerical integration. The proposed method adopts a pure minimization framework: a single neural network is trained with a loss function derived from the method of characteristics of the HJ equation. This design guarantees convergence to the optimal map while eliminating adversarial training stages, thereby substantially reducing computational complexity. Furthermore, the framework naturally extends to a wide class of cost functions and supports class-conditional transport. Extensive experiments on diverse datasets demonstrate the accuracy, scalability, and efficiency of the proposed method, establishing it as a principled and versatile tool for OT applications with provable optimality.

Social Aspects · Trustworthy Machine Learning

Ismail Lamaakal, Chaymae Yahyati, Khalid Makkaoui, Ibrahim Ouahbi, Yassine Maleh

Reliable uncertainty estimation is a key missing piece for on-device monitoring in TinyML: microcontrollers must detect failures, distribution shift, or accuracy drops under strict flash/latency budgets, yet common uncertainty approaches (deep ensembles, MC dropout, early exits, temporal buffering) typically require multiple passes, extra branches, or state that is impractical on milliwatt hardware. This paper proposes a novel and practical method, SNAP-UQ, for single-pass, label-free uncertainty estimation based on depth-wise next-activation prediction. SNAP-UQ taps a small set of backbone layers and uses tiny int8 heads to predict the mean and scale of the next activation from a low-rank projection of the previous one; the resulting standardized prediction error forms a depth-wise surprisal signal that is aggregated and mapped through a lightweight monotone calibrator into an actionable uncertainty score. The design introduces no temporal buffers or auxiliary exits and preserves state-free inference, while increasing deployment footprint by only a few tens of kilobytes. Across vision and audio backbones, SNAP-UQ reduces flash and latency relative to early-exit and deep-ensemble baselines (typically $\sim$40--60% smaller and $\sim$25--35% faster), with several competing methods at similar accuracy often exceeding MCU memory limits. On corrupted streams, it improves accuracy-drop event detection by multiple AUPRC points and maintains strong failure detection (AUROC $\approx 0.9$) in a single forward pass. By grounding uncertainty in layer-to-layer dynamics rather than solely in output confidence, SNAP-UQ offers a novel, resource-efficient basis for robust TinyML monitoring. Our code is available at: https://github.com/Ism-ail11/SNAP-UQ

Computer Vision · Classification and Understanding

Kaiting Liu, Hazel Doughty

Video recognition models are typically trained on fixed taxonomies which are often too coarse, collapsing distinctions in object, manner or outcome under a single label. As tasks and definitions evolve, such models cannot accommodate emerging distinctions and collecting new annotations and retraining to accommodate such changes is costly. To address these challenges, we introduce category splitting, a new task where an existing classifier is edited to refine a coarse category into finer subcategories, while preserving accuracy elsewhere. We propose a zero-shot editing method that leverages the latent compositional structure of video classifiers to expose fine-grained distinctions without additional data. We further show that low-shot fine-tuning, while simple, is highly effective and benefits from our zero-shot initialization. Experiments on our new video benchmarks for category splitting demonstrate that our method substantially outperforms vision-language baselines, improving accuracy on the newly split categories without sacrificing performance on the rest. Project page: https://kaitingliu.github.io/Category-Splitting/.

Computer Vision · Vision Models & Multimodal

Jianghao Yin, Qin Chen, Kedi Chen, Jie Zhou, Xingjiao Wu, Liang He

Large Vision-Language Models (LVLMs) exhibit outstanding performance on vision-language tasks but struggle with hallucination problems. Through in-depth analysis of LVLM activation patterns, we reveal two key findings: 1) truthfulness and visual perception capabilities predominantly engage different subsets of attention heads within the model architecture; and 2) truthfulness steering vectors vary significantly across different semantic contexts. Based on these observations, we propose Dynamic Multimodal Activation Steering, a training-free approach for hallucination mitigation. Our method constructs a semantic-based truthfulness steering vector database and computes visual perception steering vectors, enabling context-aware interventions during inference by dynamically selecting the most relevant steering vectors based on input semantic similarity and applying them to the most influential attention heads. We conduct comprehensive experiments across multiple models and datasets, demonstrating that our approach significantly enhances model performance, outperforming existing state-of-the-art methods.

Wendong XU, Jing Xiong, Chenyang Zhao, Qiujiang Chen, Haoran Wang, Hui Shen, Zhongwei Wan, Jianbo Dai, Taiqiang Wu, He Xiao 等

We present \textsc{SwingArena}, a adversarial evaluation framework for Large Language Models (LLMs) that closely mirrors real-world software development workflows. Unlike traditional static benchmarks, \textsc{SwingArena} models the collaborative process of software iteration by pairing LLMs as \textit{submitters}, who generate patches, and \textit{reviewers}, who create test cases and verify the patches through continuous integration (CI) pipelines. To support these interactive evaluations, we introduce a retrieval-augmented code generation (RACG) module that efficiently handles long-context challenges by providing syntactically and semantically relevant code snippets from large codebases, supporting multiple programming languages (C++, Python, Rust, and Go). This enables the framework to scale across diverse tasks and contexts while respecting token limitations. Our experiments, using over 400 high-quality real-world GitHub issues selected from a pool of 2,300 issues, show that models like GPT-4o excel at aggressive patch generation, whereas DeepSeek and Gemini prioritize correctness in CI validation. \textsc{SwingArena} presents a scalable and extensible methodology for evaluating LLMs in realistic, CI-driven software development settings.

Computer Vision · Vision Models & Multimodal

Haomin Wang, Jinhui Yin, Qi Wei, Wenguang Zeng, Lixin Gu, Shenglong Ye, Zhangwei Gao, Yaohui Wang, Yanting Zhang, Yuanqi Li 等

General SVG modeling remains challenging due to fragmented datasets, limited transferability of methods across tasks, and the difficulty of handling structural complexity. In response, we leverage the strong transfer and generalization capabilities of multimodal large language models (MLLMs) to achieve unified modeling for SVG understanding, editing, and generation. We present the InternSVG family, an integrated data–benchmark–model suite. At its core is SAgoge, the largest and most comprehensive multimodal dataset for SVG tasks, encompassing both static graphics and dynamic animations. It covers icons, long-sequence illustrations, scientific diagrams, and dynamic animations, supporting tasks of varied difficulty levels and providing deeper hierarchies with richer attributes compared to previous datasets. Based on this resource, we introduce SArena, a companion benchmark with comprehensive task definitions and standardized evaluation that aligns with the domains and difficulty spectrum covered by SAgoge. Building on these foundations, we propose InternSVG, a unified MLLM for SVG understanding, editing, and generation with SVG-specific special tokens, subword-based embedding initialization, and a two-stage training strategy that progresses from short static SVGs to long-sequence illustrations and complex animations. This unified formulation induces positive transfer and improves overall performance. Experiments on \benchset and prior benchmark confirm that InternSVG achieves substantial gains and consistently outperforms leading open and proprietary counterparts.

Computer Vision · Vision Models & Multimodal

Jack Hong, Shilin Yan, Jiayin Cai, Xiaolong Jiang, Yao Hu, Weidi Xie

We introduce WorldSense, the first benchmark to assess the multi-modal video understanding, that simultaneously encompasses visual, audio, and text inputs. In contrast to existing benchmarks, our WorldSense has several features: (i) collaboration of omni-modality, we design the evaluation tasks to feature a strong coupling of audio and video, requiring models to effectively utilize the synergistic perception of omni-modality; (ii) diversity of videos and tasks, WorldSense encompasses a diverse collection of 1,662 audio-visual synchronised videos, systematically categorized into 8 primary domains and 67 fine-grained subcategories to cover the broad scenarios, and 3,172 multi-choice QA pairs across 26 distinct tasks to enable the comprehensive evaluation; (iii) high-quality annotations, all the QA pairs are manually labeled by 80 expert annotators with multiple rounds of correction to ensure quality. Based on our WorldSense, we extensively evaluate various state-of-the-art models. The experimental results indicate that existing models face significant challenges in understanding real-world scenarios (65.1% best accuracy). By analyzing the limitations of current models, we aim to provide valuable insight to guide development of real-world understanding. We hope our WorldSense can provide a platform for evaluating the ability in constructing and understanding coherent contexts from omni-modality.

Applications · Language, Speech and Dialog

Ziyang Ma, Ruiyang Xu, Zhenghao Xing, Yunfei Chu, Yuxuan Wang, Jinzheng He, Jin Xu, Pheng-Ann Heng, Kai Yu, Junyang Lin 等

Fine-grained perception of multimodal information is critical for advancing human–AI interaction. With recent progress in audio–visual technologies, Omni Language Models (OLMs), capable of processing audio and video signals in parallel, have emerged as a promising paradigm for achieving richer understanding and reasoning. However, their capacity to capture and accurately describe fine-grained details remains limited explored. In this work, we present a systematic and comprehensive investigation of omni detailed perception from the perspectives of the data pipeline, models, and benchmark. We first identify an inherent ``co-growth'' between the level of detail and the degree of hallucination in current OLMs. To address this, we propose \textbf{Omni-Detective}, an agentic data generation pipeline integrating tool-calling, to autonomously produce highly detailed yet minimally hallucinatory multimodal data. Based on the data generated with Omni-Detective, we train two captioning models: \textbf{Audio-Captioner} for audio-only detailed perception, and \textbf{Omni-Captioner} for audio–visual detailed perception. Under the cascade evaluation protocol, Audio-Captioner achieves the best performance on MMAU and MMAR among all open-source models, surpassing Gemini 2.5 Flash and delivering performance comparable to Gemini 2.5 Pro. On existing detailed captioning benchmarks, Omni-Captioner sets a new state-of-the-art on VDC and achieves the best trade-off between detail and hallucination on the video-SALMONN 2 testset. Given the absence of a dedicated benchmark for omni detailed perception, we design \textbf{Omni-Cloze}, a novel cloze-style evaluation for detailed audio, visual, and audio-visual captioning that ensures stable, efficient, and reliable assessment. Experimental results and analysis demonstrate the effectiveness of Omni-Detective in generating high-quality detailed captions, as well as the superiority and human preference alignment of Omni-Cloze in evaluating such detailed captions. All the data pipeline, models, and the benchmark are open-source to facilitate further research for omni detailed perception.\footnote{\url{https://github.com/ddlBoJack/Omni-Captioner}}

Computer Vision · Vision Models & Multimodal

Eun Woo Im, Muhammad Kashif Ali, Vivek Gupta

Large Vision-Language Models (LVLMs) have demonstrated remarkable multimodal capabilities, but they inherit the tendency to hallucinate from their underlying language models. While visual contrastive decoding has been proposed to mitigate this issue, existing methods often apply generic visual augmentations that disregard the specific context provided by the text query, limiting their effectiveness. This study introduces a novel training-free decoding strategy that addresses these limitations, featuring two key contributions. First, a self-augmentation prompting strategy that leverages the intrinsic knowledge of the model to dynamically align semantics between the query and the visual augmentation. Second, an adaptive thresholding algorithm that adaptively adjusts next token candidate size based on the output sparsity, utilizing full information from the logit distribution. Extensive experiments across four LVLMs and seven benchmarks demonstrate that the proposed decoding significantly enhances factual consistency compared to state-of-the-art decoding methods. This work highlights the importance of integrating query-dependent augmentation and entropy-aware decoding for improving effective generation of LVLMs. The source code will be released upon acceptance.

General Machine Learning · Representation Learning

Yunhe Zhang, Jinyu Cai, Qi Hao, Pengyang Wang, See-Kiong Ng

Graph outlier detection is a critical task for identifying rare, deviant patterns in graph-structured data. However, prevalent methods based on graph convolution are fundamentally challenged by the ''Homophily Trap'': the aggregation of features from neighboring nodes inadvertently contaminates the representations of normal nodes near anomalies, blurring their distinctions. To overcome this limitation, we propose a Clustering-guided Edge Reweighting framework for Graph Outlier Detection (CER-GOD), which jointly optimizes a self-discriminative masking spoiler with an adaptive clustering-based outlier detector. The masking spoiler learns to selectively weaken the influence of heterogeneous neighbors, preserving the discriminative power of node embeddings. This process is guided by the clustering detector, which generates pseudo-labels in an unsupervised manner, thereby eliminating the need for predefined anomaly thresholds. To ensure robust optimization and prevent class collapse—a failure mode exacerbated by the homophily trap—we introduce a diversity loss that stabilizes the clustering process. Our end-to-end framework demonstrates superior performance on multiple benchmark datasets, establishing a new state-of-the-art by effectively dismantling the homophily trap.

Optimization · Non-Convex

Francisco Patitucci, Ruichen Jiang, Aryan Mokhtari

A recent breakthrough in nonconvex optimization is the online-to-nonconvex conversion framework of Cutkosky et al. (2023), which reformulates the task of finding an $\varepsilon$-first-order stationary point as an online learning problem. When both the gradient and the Hessian are Lipschitz continuous, instantiating this framework with two different online learners achieves a complexity of $ \mathcal{O}(\varepsilon^{-1.75}\log(1/\varepsilon)) $ in the deterministic case and a complexity of $ \mathcal{O}(\varepsilon^{-3.5}) $ in the stochastic case. However, this approach suffers from several limitations: (i) the deterministic method relies on a complex double-loop scheme that solves a fixed-point equation to construct hint vectors for an optimistic online learner, introducing an extra logarithmic factor; (ii) the stochastic method assumes a bounded second-order moment of the stochastic gradient, which is stronger than standard variance bounds; and (iii) different online learning algorithms are used in the two settings. In this paper, we address these issues by introducing an online optimistic gradient method based on a novel **doubly optimistic hint function**. Specifically, we use the gradient at an extrapolated point as the hint, motivated by two optimistic assumptions: that the difference between the hint and the target gradient remains near constant, and that consecutive update directions change slowly due to smoothness. Our method eliminates the need for a double loop and removes the logarithmic factor. Furthermore, by simply replacing full gradients with stochastic gradients and under the standard assumption that their variance is bounded by $\sigma^2$, we obtain a unified algorithm with complexity $\mathcal{O}(\varepsilon^{-1.75} + \sigma^2 \varepsilon^{-3.5})$, smoothly interpolating between the best-known deterministic rate and the optimal stochastic rate.

Computer Vision · Vision Models & Multimodal

Jianping Zhong, Zhaobo Qi, Kaiwen Duan, Xinyan Liu, Beichen Zhang, Weigang Zhang, Qingming Huang

3D object detection from LiDAR point cloud data is important for autonomous driving systems. Recent two-stage 3D object detectors struggle to achieve satisfactory performance due to limitations in proposal quality, stemming from the degradation of geometric detail information in the generated proposal features caused by high sparsity and uneven distribution of point clouds, as well as a lack of effective exploitation of surrounding contextual cues in the independent proposal refinement stage. To this end, we propose a Proposal-centric Transformer Network (PTN), which includes a Hierarchical Attentive Feature Alignment (HAFA) module and a Collaborative Proposal Refinement Module (CPRM). More concretely, to obtain multi-granularity proposal representations, HAFA employs a dual-stream architecture that extracts both coarse-grained voxel features and fine-grained point features to enhance proposal features, then harmo- nizes them through a feature alignment network in a unified space. The CPRM first generates object queries for all objects and then establishes contextual-aware interactions to extract complementary information from semantically similar and spatially relevant proposals. PTN achieves promising performance on large-scale Waymo and KITTI benchmark, demonstrating the superiority of PTN.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Georgi Ganev, MohammadReza Nazari, Rees Davison, Amirhassan Dizche, XINMIN WU, Ralph Abbey, Jorge Silva, Emiliano De Cristofaro

The Synthetic Minority Over-sampling Technique (SMOTE) is one of the most widely used methods for addressing class imbalance and generating synthetic data. Despite its popularity, little attention has been paid to its privacy implications; yet, it is used in the wild in many privacy-sensitive applications. In this work, we conduct the first systematic study of privacy leakage in SMOTE: We begin by showing that prevailing evaluation practices, i.e., naive distinguishing and distance-to-closest-record metrics, completely fail to detect any leakage and that membership inference attacks (MIAs) can be instantiated with high accuracy. Then, by exploiting SMOTE's geometric properties, we build two novel attacks with very limited assumptions: DistinSMOTE, which perfectly distinguishes real from synthetic records in augmented datasets, and ReconSMOTE, which reconstructs real minority records from synthetic datasets with perfect precision and recall approaching one under realistic imbalance ratios. We also provide theoretical guarantees for both attacks. Experiments on eight standard imbalanced datasets confirm the practicality and effectiveness of these attacks. Overall, our work reveals that SMOTE is inherently non-private and disproportionately exposes minority records, highlighting the need to reconsider its use in privacy-sensitive applications and as a baseline for assessing the privacy of modern generative models.

RUIYANG ZHANG, Dongzhan Zhou, Zhedong Zheng

Despite the empirical success of extensive, step-by-step reasoning in large multimodal models, long reasoning processes inevitably incur substantial computational overhead, i.e., in terms of higher token costs and increased response time, which undermines inference efficiency. In contrast, humans often employ sketch-style reasoning: a concise, goal-directed cognitive process that prioritizes salient information and enables efficient problem-solving. Inspired by this cognitive efficiency, we propose SketchThinker-R1, which incentivizes sketch-style reasoning ability in large multimodal models. Our method consists of three primary stages. In the Sketch-Mode Cold Start stage, we convert standard long reasoning process into sketch-style reasoning and finetune base multimodal model, instilling initial sketch-style reasoning capability. Next, we train SketchJudge Reward Model, which explicitly evaluates thinking process of model and assigns higher scores to sketch-style reasoning. Finally, we conduct Sketch-Thinking Reinforcement Learning under supervision of SketchJudge to further generalize sketch-style reasoning ability. Experimental evaluation on four benchmarks reveals that our SketchThinker-R1 achieves over 64% reduction in reasoning token cost without compromising final answer accuracy. Qualitative analysis further shows that sketch-style reasoning focuses more on key cues during problem solving.

General Machine Learning · Transfer, Multitask and Meta-learning

Yupeng Chang, Yi Chang, Yuan Wu

Parameter-efficient fine-tuning (PEFT) has become a *de facto* standard for adapting Large Language Models (LLMs). However, we identify a critical vulnerability within popular low-rank adaptation methods such as LoRA: they can exacerbate ``Catastrophic Inheritance''---the unchecked propagation of biases, noise, and data imbalances from pre-training. This phenomenon can degrade model robustness and fairness, undermining the benefits of efficient adaptation. To address this, we introduce Bias-Alleviating Low-Rank Adaptation (BA-LoRA). Our approach is founded on a principled decomposition of Catastrophic Inheritance into three core challenges: Knowledge Drift, Representation Collapse, and Overfitting to Noise. BA-LoRA systematically mitigates these issues by incorporating a trio of targeted regularizers: consistency, diversity, and an SVD-based term, designed to preserve core knowledge, enforce representational richness, and promote robust, low-rank output representations, respectively. We conduct comprehensive evaluations on a suite of Natural Language Generation (NLG) and Understanding (NLU) tasks using diverse, prominent open-source language models (e.g., LLaMA-2-7B and DeBERTa-v3-base). Our results show that BA-LoRA not only outperforms state-of-the-art LoRA variants in terms of performance and stability, but also demonstrates superior robustness and bias mitigation on targeted evaluations. These results provide evidence that BA-LoRA can counteract the adverse effects of Catastrophic Inheritance. Code is available at https://github.com/llm172/BA-LoRA.

Optimization · Learning for Optimization

Chaolong Ying, Yingqi Ruan, Xuemin Chen, Yaomin Wang, Tianshu Yu

The Maximum Common Edge Subgraph (MCES) problem is a crucial challenge with significant implications in domains such as biology and chemistry. Traditional approaches, which include transformations into max-clique and search-based algorithms, suffer from scalability issues when dealing with larger instances. This paper introduces ``Neural Graduated Assignment'' (NGA), a simple, scalable, unsupervised-training-based method that addresses these limitations. Central to NGA is stacking of differentiable assignment optimization with neural components, enabling high-dimensional parameterization of the matching process through a learnable temperature mechanism. We further theoretically analyze the learning dynamics of NGA, showing its design leads to fast convergence, better exploration-exploitation tradeoff, and ability to escape local optima. Extensive experiments across MCES computation, graph similarity estimation, and graph retrieval tasks reveal that NGA not only significantly improves computation time and scalability on large instances but also enhances performance compared to existing methodologies. The introduction of NGA marks a significant advancement in the computation of MCES and offers insights into other assignment problems.

Optimization · Everything Else

Albert Catalan-Tatjer, Niccolò Ajroldi, Jonas Geiping

While post-training quantization is widely adopted for efficient deployment of large language models, the mechanisms underlying quantization robustness remain unclear. We conduct a comprehensive analysis of quantization degradation across open-source language model training trajectories up to 32B parameters and 15T training tokens to accurately assess the relationship between training dynamics and quantization performance. Our key finding is that quantization errors in large-scale training runs are driven by a complex interplay between learning rate and other training hyperparameters. Specifically, once learning rates decay, validation loss and quantization error diverge, largely independent of training data scale. To investigate interventions on the training dynamics and identify specific configurations that can modulate quantization robustness favorably, we train our own models in controlled experiments up to 100B tokens. Our results challenge the assumption that increasing dataset scale inherently compromises quantization effectiveness, demonstrating instead that strategic training hyperparameter interventions can improve quantization quality at scale.

Deep Learning · Attention Mechanisms

Chen Zhang, Jianghui Wang, Bingyang Cheng, Zhongtao Chen, Wendong XU, Cong Wang, Marco Canini, Francesco Orabona, Yik-Chung WU, Ngai Wong

Attention learners, neural networks built on the attention mechanism, e.g., transformers, excel at learning the implicit relationships that relate sequences to their corresponding properties, e.g., mapping a given sequence of tokens to the probability of the next token. However, the learning process tends to be costly. To address this, we present a novel paradigm named **Atte**ntion **N**eural **T**eaching (AtteNT) that reinterprets the learning process through a nonparametric teaching perspective. Specifically, the latter provides a theoretical framework for teaching mappings that are implicitly defined (i.e., nonparametric) via example selection. Such an implicit mapping is embodied through a dense set of sequence-property pairs, with the AtteNT teacher selecting a subset to accelerate convergence in attention learner training. By analytically investigating the role of attention on parameter-based gradient descent during training, and recasting the evolution of attention learners, shaped by parameter updates, through functional gradient descent in nonparametric teaching, we show *for the first time* that teaching attention learners is consistent with teaching importance-adaptive nonparametric learners. These new findings readily commit AtteNT to enhancing learning efficiency of attention learners. Specifically, we observe training time reductions of 13.01% for LLMs and 20.58% for ViTs, spanning both fine-tuning and training-from-scratch regimes. Crucially, these gains are achieved without compromising accuracy; in fact, performance is consistently preserved and often enhanced across a diverse set of downstream tasks.

Optimization · Optimization and Learning under Uncertainty

Tianming Zhao, Albert Zomaya

Algorithms with predictions leverage predictions for unknown inputs in online decision-making. These algorithms are analyzed by consistency, i.e., competitive ratio under perfect predictions, and robustness, i.e., competitive ratio under worst-case predictions. Smooth degrading performance with an increased prediction error is also desirable. This paper refines the notion of smoothness, a function of prediction error, defined as the competitive ratio over the problem instances where predictions are guaranteed to provide additional information. With our refined smoothness metric, we establish smoothness bounds for a few scheduling problems, including online total completion time minimization and makespan minimization. For a single machine to minimize the total completion time, we show a lower bound of $\eta$ and a $\eta^2$-smooth algorithm, where $\eta$ is the prediction error ($\eta \geq 1$); the bound holds for small errors. For parallel identical machines to minimize the makespan, we show a lower bound of $2 - O(\eta^{-2})$ and present an $O(\eta^2)$-smooth algorithm for small errors. Both bounds are tighter than the existing ones. For uniformly-related machines to minimize the makespan, we show a tight lower bound of $\lceil \log \eta \rceil$, matched by an $O(\log \eta)$-smooth algorithm.