Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared to the classical $\ell_1$-Calibration while still having strong implications for downstream applications. One recent such example is the work by Fishelson et al. (2025) who show that it is possible to achieve $O(T^{1/3})$ pseudo $\ell_2$-Calibration error via minimizing pseudo swap regret of the squared loss, which in fact implies the same bound for all bounded proper losses with a smooth univariate form. In this work, we significantly generalize their result in the following ways: (a) in addition to smooth univariate forms, our algorithm also simultaneously achieves $O(T^{1/3})$ swap regret for any proper loss with a twice continuously differentiable univariate form (such as Tsallis entropy); (b) our bounds hold not only for pseudo swap regret that measures losses using the forecaster's distributions on predictions, but also hold for the actual swap regret that measures losses using the forecaster's actual realized predictions. We achieve so by introducing a new stronger notion of calibration called (pseudo) KL-Calibration, which we show is equivalent to the (pseudo) swap regret for log loss. We prove that there exists an algorithm that achieves $O(T^{1/3})$ KL-Calibration error and provide an explicit algorithm that achieves $O(T^{1/3})$ pseudo KL-Calibration error. Moreover, we show that the same algorithm achieves $O(T^{1/3}(\log T)^{-1/3}\log(T/\delta))$ swap regret w.p. $\ge 1-\delta$ for any proper loss with a smooth univariate form, which implies $O(T^{1/3})$ $\ell_2$-Calibration error. A technical contribution of our work is a new randomized rounding procedure and a non-uniform discretization scheme to minimize the swap regret for log loss.

Linear representation hypothesis posits that high-level concepts are encoded as linear directions in the representation spaces of LLMs. Park et al. (2024) formalize this notion by unifying multiple interpretations of linear representation, such as 1-dimensional subspace representation and interventions, using a causal inner product. However, their framework relies on single-token counterfactual pairs and cannot handle ambiguous contrasting pairs, limiting its applicability to complex or context-dependent concepts. We introduce a new notion of binary concepts as unit vectors in a canonical representation space, and utilize LLMs' (neural) activation differences along with maximum likelihood estimation (MLE) to compute concept directions (i.e., steering vectors). Our method, Sum of Activation-base Normalized Difference (SAND), formalizes the use of activation differences modeled as samples from a von Mises-Fisher (vMF) distribution, providing a principled approach to derive concept directions. We extend the applicability of Park et al. (2024) by eliminating the dependency on unembedding representations and single-token pairs. Through experiments with LLaMA models across diverse concepts and benchmarks, we demonstrate that our lightweight approach offers greater flexibility, superior performance in activation engineering tasks like monitoring and manipulation.

To compare autoregressive language models at scale, we propose using log-likelihood vectors computed on a predefined text set as model features. This approach has a solid theoretical basis: when treated as model coordinates, their squared Euclidean distance approximates the Kullback-Leibler divergence of text-generation probabilities. Our method is highly scalable, with computational cost growing linearly in both the number of models and text samples, and is easy to implement as the required features are derived from cross-entropy loss. Applying this method to over 1,000 language models, we constructed a "model map," providing a new perspective on large-scale model analysis.

This paper presents linear DML models for causal inference using the simplest Python code on a Jupyter notebook based on an Anaconda platform and compares the performance of different DML models. The results show that current Library API technology is not yet sufficient to enable novice Python users to build qualified and high-quality DML models with the simplest coding approach. Novice users attempting to perform DML causal inference using Python still have to improve their mathematical and computer knowledge to adapt to more flexible DML programming. Additionally, the issue of mismatched outcome variable dimensions is also widespread when building linear DML models in Jupyter notebook.

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves stateof-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.

Data valuation is increasingly used in machine learning (ML) to decide the fair compensation for data owners and identify valuable or harmful data for improving ML models. Cooperative game theory-based data valuation, such as Data Shapley, requires evaluating the data utility (e.g., validation accuracy) and retraining the ML model for multiple data subsets. While most existing works on efficient estimation of the Shapley values have focused on reducing the number of subsets to evaluate, our framework, \texttt{DUPRE}, takes an alternative yet complementary approach that reduces the cost per subset evaluation by predicting data utilities instead of evaluating them by model retraining. Specifically, given the evaluated data utilities of some data subsets, \texttt{DUPRE} fits a \emph{Gaussian process} (GP) regression model to predict the utility of every other data subset. Our key contribution lies in the design of our GP kernel based on the sliced Wasserstein distance between empirical data distributions. In particular, we show that the kernel is valid and positive semi-definite, encodes prior knowledge of similarities between different data subsets, and can be efficiently computed. We empirically verify that \texttt{DUPRE} introduces low prediction error and speeds up data valuation for various ML models, datasets, and utility functions.

In this paper, an improved clustering technique for large textual datasets by leveraging fine-tuned word embeddings is presented. WEClustering technique is used as the base model. WEClustering model is fur-ther improvements incorporating fine-tuning contextual embeddings, advanced dimensionality reduction methods, and optimization of clustering algorithms. Experimental results on benchmark datasets demon-strate significant improvements in clustering metrics such as silhouette score, purity, and adjusted rand index (ARI). An increase of 45% and 67% of median silhouette score is reported for the proposed WE-Clustering_K++ (based on K-means) and WEClustering_A++ (based on Agglomerative models), respec-tively. The proposed technique will help to bridge the gap between semantic understanding and statistical robustness for large-scale text-mining tasks.

Target tracking entails the estimation of the evolution of the target state over time, namely the target trajectory. Different from the classical state space model, our series of studies, including this paper, model the collection of the target state as a stochastic process (SP) that is further decomposed into a deterministic part which represents the trend of the trajectory and a residual SP representing the residual fitting error. Subsequently, the tracking problem is formulated as a learning problem regarding the trajectory SP for which a key part is to estimate a trajectory FoT (T-FoT) best fitting the measurements in time series. For this purpose, we consider the polynomial T-FoT and address the regularized polynomial T-FoT optimization employing two distinct regularization strategies seeking trade-off between the accuracy and simplicity. One limits the order of the polynomial and then the best choice is determined by grid searching in a narrow, bounded range while the other adopts $\ell_0$ norm regularization for which the hybrid Newton solver is employed. Simulation results obtained in both single and multiple maneuvering target scenarios demonstrate the effectiveness of our approaches.

X, SEPTEMBER XXXX 1 Set a Thief to Catch a Thief: Combating Label Noise through Noisy Meta Learning Hanxuan Wang, Na Lu, Xueying Zhao, Y uxuan Y an, Kaipeng Ma, Kwoh Chee Keong, Gustavo Carneiro Abstract --Learning from noisy labels (LNL) aims to train high-performance deep models using noisy datasets. Meta learning based label correction methods have demonstrated remarkable performance in LNL by designing various meta label rectification tasks. However, extra clean validation set is a prerequisite for these methods to perform label correction, requiring extra labor and greatly limiting their practicality. T o tackle this issue, we propose a novel noisy meta label correction framework STCT, which counterintuitively uses noisy data to correct label noise, borrowing the spirit in the saying " S et a T hief to C atch a T hief". The core idea of STCT is to leverage noisy data which is i.i.d. with the training data as a validation set to evaluate model performance and perform label correction in a meta learning framework, eliminating the need for extra clean data. By decoupling the complex bi-level optimization in meta learning into representation learning and label correction, STCT is solved through an alternating training strategy between noisy meta correction and semi-supervised representation learning. Extensive experiments on synthetic and real-world datasets demonstrate the outstanding performance of STCT, particularly in high noise rate scenarios. STCT achieves 96.9% label correction and 95.2% classification performance on CIF AR-10 with 80% symmetric noise, significantly surpassing the current state-of-the-art. I NTRODUCTION D EEP Deep learning has achieved great success in various fields, attributed to the availability of carefully annotated large scale datasets [1], [2], [3]. However, the collection of high quality datasets generally comes with high annotation cost and intensive human intervention, creating a significant obstacle to the development of deep learning. Fortunately, the annotation cost issue can be mitigated through web crawling [4] and crowdsourcing [5]. However, such low-cost datasets often contain a considerable amount of noisy labels, which may lead to severe overfitting of neural networks and performance degradation [6].

Multilingual audio-text retrieval (ML-ATR) is a challenging task that aims to retrieve audio clips or multilingual texts from databases. However, existing ML-ATR schemes suffer from inconsistencies for instance similarity matching across languages. We theoretically analyze the inconsistency in terms of both multilingual modal alignment direction error and weight error, and propose the theoretical weight error upper bound for quantifying the inconsistency. Based on the analysis of the weight error upper bound, we find that the inconsistency problem stems from the data distribution error caused by random sampling of languages. We propose a consistent ML-ATR scheme using 1-to-k contrastive learning and audio-English co-anchor contrastive learning, aiming to mitigate the negative impact of data distribution error on recall and consistency in ML-ATR. Experimental results on the translated AudioCaps and Clotho datasets show that our scheme achieves state-of-the-art performance on recall and consistency metrics for eight mainstream languages, including English. Our code will be available at https://github.com/ATRI-ACL/ATRI-ACL.