Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their applicability in proprietary or large-scale settings. We propose a nonparametric attribution method that operates entirely on data, measuring influence via patch-level similarity between generated and training images. Our approach is grounded in the analytical form of the optimal score function and naturally extends to multiscale representations, while remaining computationally efficient through convolution-based acceleration. In addition to producing spatially interpretable attributions, our framework uncovers patterns that reflect intrinsic relationships between training data and outputs, independent of any specific model. Experiments demonstrate that our method achieves strong attribution performance, closely matching gradient-based approaches and substantially outperforming existing nonparametric baselines. Code is available at https://github.com/sail-sg/NDA.

Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain widely used for their robustness in low-data regimes and transparent theoretical grounding. Despite extensive studies of kernel spectra in machine learning, systematic spectral analyses of molecular kernels are scarce. In this work, we provide the first comprehensive spectral analysis of kernel ridge regression on the QM9 dataset, molecular fingerprint, pretrained transformer-based, global and local 3D representations across seven molecular properties. Surprisingly, richer spectral features, measured by four different spectral metrics, do not consistently improve accuracy. Pearson correlation tests further reveal that for transformer-based and local 3D representations, spectral richness can even have a negative correlation with performance. We also implement truncated kernels to probe the relationship between spectrum and predictive performance: in many kernels, retaining only the top 2% of eigenvalues recovers nearly all performance, indicating that the leading eigenvalues capture the most informative features. Our results challenge the common heuristic that "richer spectra yield better generalization" and highlight nuanced relationships between representation, kernel features, and predictive performance. Beyond molecular property prediction, these findings inform how kernel and self-supervised learning methods are evaluated in data-limited scientific and real-world tasks.

The stop gradient and exponential moving average iterative procedures are commonly used in non-contrastive approaches to self-supervised learning to avoid representation collapse, with excellent performance in downstream applications in practice. This presentation investigates these procedures from the dual viewpoints of optimization and dynamical systems. We show that, in general, although they do not optimize the original objective, or any other smooth function, they do avoid collapse Following Tian et al. (2021), but without any of the extra assumptions used in their proofs, we then show using a dynamical system perspective that, in the linear case, minimizing the original objective function without the use of a stop gradient or exponential moving average always leads to collapse. Conversely, we characterize explicitly the equilibria of the dynamical systems associated with these two procedures in this linear setting as algebraic varieties in their parameter space, and show that they are, in general, asymptotically stable . Our theoretical findings are illustrated by empirical experiments with real and synthetic data. Self-supervised learning (or SSL) is an approach to representation learning that exploits the internal consistency of training data without requiring expensive annotations. However, non-contrastive approaches to SSL (Assran et al., 2023; Bardes et al., 2022) that take as input different views of the same data samples and learn to predict one view from the other, are susceptible to representational collapse where a constant embedding is learned for all data points (LeCun, 2022). We use in this presentation the dual viewpoints of optimization and dynamical systems to study theoretically and empirically the well-known stop gradient (Chen and He, 2021) and exponential moving average (Grill et al., 2020) training procedures that are specifically designed to avoid this problem. Here C is the global minimum of E (θ,ψ) (shown as negative instead of zero for readibility) associated with a collapse of the training process; B is a nontrivial local minimum one may reach using an appropriate regularization to avoid collapse; and A is a limit point of the stop gradient (SG) training procedure associated with parameters θ and ψ at convergence. In general, it is not a minimum of E and thus does not correspond to a collapse of the training process, but it is a minimum with respect to ψ of E ( θ,ψ).

Humans understand new combinations of words encountered if they are combinations of words recognized from different contexts, an ability called Compositional Generalization. The COGS benchmark (Kim and Linzen, 2020) arXiv:2010.05465 reports 0% accuracy for Transformer models on some structural generalizations. We use (Weiss et al., 2021) arXiv:2106.06981's Restricted Access Sequence Processing (RASP), a Transformer-equivalent programming language, to demonstrate that a Transformer Encoder-Decoder can perform COGS and the semantically equivalent ReCOGS_pos (Wu et al., 2024) arXiv:2303.13716 systematically and compositionally: Our RASP models attain near perfect scores on structural generalization splits on COGS (exact match) and ReCOGS_pos (semantic exact match). Our RASP models show the (Re)COGS tasks do not require a hierarchical or tree-structured solution (contrary to (Kim and Linzen, 2020) arXiv:2010.05465, (Yao and Koller, 2022) arXiv:2210.13050, (Murty et al., 2022) arXiv:2211.01288, (Liu et al., 2021) arXiv:2107.06516): we use word-level tokens with an "embedding" layer that tags with possible part of speech, applying just once per encoder pass 19 attention-head compatible flat pattern-matching rules (easily identified with specific training examples), shown using grammar coverage (Zeller et al., 2023) to cover the non-recursive aspects of the input grammar, plus masking out prepositional phrases ("pp noun") and/or sentential complements (cp) when recognizing grammar patterns and extracting nouns related to the main verb in the sentence, and output the next logical form (LF) token (repeating until the LF is complete). The models do not apply recursive, tree-structured rules like "np_det pp np -> np_pp -> np", but score near perfect semantic and string exact match on both COGS and ReCOGS pp recursion, cp recursion using the decoder loop.

Abnormal stop detection (ASD) in intercity coach transportation is critical for ensuring passenger safety, operational reliability, and regulatory compliance. However, two key challenges hinder ASD effectiveness: sparse GPS trajectories, which obscure short or unauthorized stops, and limited labeled data, which restricts supervised learning. Existing methods often assume dense sampling or regular movement patterns, limiting their applicability. To address data sparsity, we propose a Sparsity-Aware Segmentation (SAS) method that adaptively defines segment boundaries based on local spatial-temporal density. Building upon these segments, we introduce three domain-specific indicators to capture abnormal stop behaviors. To further mitigate the impact of sparsity, we develop Locally Temporal-Indicator Guided Adjustment (LTIGA), which smooths these indicators via local similarity graphs. To overcome label scarcity, we construct a spatial-temporal graph where each segment is a node with LTIGA-refined features. We apply label propagation to expand weak supervision across the graph, followed by a GCN to learn relational patterns. A final self-training module incorporates high-confidence pseudo-labels to iteratively improve predictions. Experiments on real-world coach data show an AUC of 0.854 and AP of 0.866 using only 10 labeled instances, outperforming prior methods. The code and dataset are publicly available at \href{https://github.com/pangjunbiao/Abnormal-Stop-Detection-SSL.git}

A critical aspect of analyzing and improving modern machine learning systems lies in understanding how individual training examples influence a model's predictive behavior. Estimating this influence enables critical applications, including data selection and model debugging; in particular, self-influence, which quantifies the influence of a training point on itself, has found many uses in data quality assessment and outlier detection. Existing methods for measuring data influence, however, are often impractical for large models due to low accuracy or prohibitive computational costs: most approaches either provide poor approximations or rely on gradients and inverse-Hessian computations that remain challenging to scale. In this work, we introduce a highly efficient zeroth-order approximation for estimating the influence of training data that requires only a fraction of the time and memory footprint of prior methods. Notably, our method relies solely on loss values of intermediate checkpoints on the training and test data, along with the checkpoints themselves, making it broadly applicable even when the loss function of interest is non-differentiable. Beyond its computational efficiency, our approach achieves superior accuracy in estimating self-influence and comparable or improved accuracy in estimating train-test influence for fine-tuned large language models, enabling scalable and practical analysis of how training data shapes model behavior.

Collecting high-quality training examples for language model fine-tuning is expensive, with practical budgets limiting the amount of data that can be procured. We investigate whether example difficulty affects GRPO training effectiveness by comparing selection strategies (easy, medium, hard, random) across multiple models and reasoning tasks. Training on the hardest 10\% of examples (those where the base model fails most often) yields dramatic performance gains up to 47\%, while easy examples produce minimal improvements of 3-15\%. This occurs because GRPO requires outcome variance to generate learning signals; hard examples maintain mixed success/failure outcomes throughout training while easy examples quickly converge to consistent success, eliminating learning opportunities. Moreover, models trained on hard examples show superior out-of-distribution generalization, with only hard-trained models achieving meaningful gains on the AIME2025 benchmark. Our findings provide clear guidance: when budget-constrained, prioritize collecting and annotating examples where your base model struggles, as these drive nearly all learning value in GRPO fine-tuning

Instance discrimination is a self-supervised representation learning paradigm wherein individual instances within a dataset are treated as distinct classes. This is typically achieved by generating two disparate views of each instance by applying stochastic transformations, which encourages the model to learn representations that are invariant to the common underlying object across these views. While this approach facilitates the acquisition of invariant representations for dataset instances under various handcrafted transformations (e.g., random cropping, color jittering), an exclusive reliance on such data transformations for achieving invariance may inherently limit the model's generalization to unseen datasets and diverse downstream tasks. The inherent limitation stems from the fact that the finite set of transformations within the data processing pipeline is unable to encompass the full spectrum of potential data variations. In this study, we provide the technical foundation for leveraging semantic pairs to enhance the generalization of the model's representation and empirically demonstrate that incorporating semantic pairs mitigates the issue of limited transformation coverage. Specifically, we propose that exposing the model to semantic pairs (i.e., two instances belonging to the same semantic category) introduces varied real-world scene contexts, thereby fostering the development of more generalizable object representations. To validate this hypothesis, we constructed and released a novel dataset comprising curated semantic pairs and conducted extensive experimentation to empirically establish that their inclusion enables the model to learn more general representations, ultimately leading to improved performance across diverse downstream tasks.

Reasoning is an important task for large language models (LLMs). Among all the reasoning paradigms, inductive reasoning is one of the fundamental types, which is characterized by its particular-to-general thinking process and the non-uniqueness of its answers. The inductive mode is crucial for knowledge generalization and aligns better with human cognition, so it is a fundamental mode of learning, hence attracting increasing interest. Despite the importance of inductive reasoning, there is no systematic summary of it. Therefore, this paper presents the first comprehensive survey of inductive reasoning for LLMs. First, methods for improving inductive reasoning are categorized into three main areas: post-training, test-time scaling, and data augmentation. Then, current benchmarks of inductive reasoning are summarized, and a unified sandbox-based evaluation approach with the observation coverage metric is derived. Finally, we offer some analyses regarding the source of inductive ability and how simple model architectures and data help with inductive tasks, providing a solid foundation for future research.

Modeling multi-modal time-series data is critical for capturing system-level dynamics, particularly in biosignals where modalities such as ECG, PPG, EDA, and accelerometry provide complementary perspectives on interconnected physiological processes. While recent self-supervised learning (SSL) advances have improved unimodal representation learning, existing multi-modal approaches often rely on CLIP-style contrastive objectives that overfit to easily aligned features and misclassify valid cross-modal relationships as negatives, resulting in fragmented and non-generalizable embeddings. To overcome these limitations, we propose ProtoMM, a novel SSL framework that introduces a shared prototype dictionary to anchor heterogeneous modalities in a common embedding space. By clustering representations around shared prototypes rather than explicit negative sampling, our method captures complementary information across modalities and provides a coherent "common language" for physiological signals. In this work, we focus on developing a Pulse Motion foundation model with ProtoMM and demonstrate that our approach outperforms contrastive-only and prior multimodal SSL methods, achieving state-of-the-art performance while offering improved interpretability of learned features. Digital biomarkers (for stress, physical activity, sleep, etc.) obtained from wearable sensors, such as smart watches and smartphones, provide unprecedented opportunities to give individuals novel insights into their states of health and wellness throughout their daily life, along with new tools for managing their health-related behaviors (Rehg et al., 2017). In order to realize this potential, however, it is critical to develop effective models for multi-modal time series biosignal data, so that complementary sensing modalities can be leveraged to overcome the ambiguities and noise that are inherent in wearable signals collected in the field environment. Recently, there has been substantial progress in developing unimodal Foundation Models (FMs) which are pre-trained using large datasets on modalities such as accelerometry (Xu et al.; Y uan et al., 2024), ECG (Abbaspourazad et al., 2023; McKeen et al., 2024), and PPG (Saha et al., 2025; Pillai et al., 2024). These models have demonstrated effective generalization to downstream tasks and have established new benchmarks for performance.