Vision-Language-Action (VLA) models trained on large robot datasets promise general-purpose, robust control across diverse domains and embodiments. However, existing approaches often fail out-of-the-box when deployed in novel environments, embodiments, or tasks. We introduce Mixture of Skills VLA (MoS-VLA), a framework that represents robot manipulation policies as linear combinations of a finite set of learned basis functions. During pretraining, MoS-VLA jointly learns these basis functions across datasets from the Open X-Embodiment project, producing a structured skill space. At test time, adapting to a new task requires only a single expert demonstration. The corresponding skill representation is then inferred via a lightweight convex optimization problem that minimizes the L1 action error, without requiring gradient updates. Empirically, MoS-VLA achieves lower action-prediction error on five out of five unseen datasets and succeeds in both simulation and real-robot tasks where a pretrained VLA model fails outright. Inspired by the success of large language models, modern robotics aims to achieve generalization and human-like performance through the use of internet-scale data and large, attention-based architectures. To this end, researchers have collected enormous datasets of robotic arm trajectories (Open X-Embodiment Collaboration et al., 2023) and trained so-called vision-language-action foundation models to map natural language task descriptions and state observations to robot actions (Kim et al., 2024; Octo Model Team et al., 2024; Brohan et al., 2023b;a; Ma et al., 2024).

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods. Our code is available at https://github.com/sxq/Heteroscedastic-Pseudo-Labels.

This manuscript has been accepted in IEEE Transactions on Industrial Informatics. Personal use of this material is permitted. Abstract--Accurate battery capacity estimation is key to alleviating consumer concerns about battery performance and reliability of electric vehicles (EVs). However, practical data limitations imposed by stringent privacy regulations and labeled data shortages hamper the development of generalizable capacity estimation models that remain robust to real-world data distribution shifts. While self-supervised learning can leverage unlabeled data, existing techniques are not particularly designed to learn effectively from challenging field data--let alone from privacy-friendly data, which are often less feature-rich and noisier . In this work, we propose a first-of-its-kind capacity estimation model based on self-supervised pre-training, developed on a large-scale dataset of privacy-friendly charging data snippets from real-world EV operations. Our pre-training framework, snippet similarity-weighted masked input reconstruction, is designed to learn rich, generalizable representations even from less feature-rich and fragmented privacy-friendly data. Our key innovation lies in harnessing contrastive learning to first capture high-level similarities among fragmented snippets that otherwise lack meaningful context. With our snippet-wise contrastive learning and subsequent similarity-weighted masked reconstruction, we are able to learn rich representations of both granular charging patterns within individual snippets and high-level associative relationships across different snippets. Bolstered by this rich representation learning, our model consistently outperforms state-of-the-art baselines, achieving 31.9%

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