Large vision-language models (LVLMs) have achieved remarkable performance on multimodal tasks. However, they still suffer from hallucinations, generating text inconsistent with visual input, posing significant risks in real-world applications. Existing approaches to address this issue focus on incorporating external knowledge bases, alignment training, or decoding strategies, all of which require substantial computational cost and time. Recent works try to explore more efficient alternatives by adjusting LVLMs' internal representations. Although promising, these methods may cause hallucinations to be insufficiently suppressed or lead to excessive interventions that negatively affect normal semantics. In this work, we leverage sparse autoencoders (SAEs) to identify semantic directions closely associated with faithfulness or hallucination, extracting more precise and disentangled hallucination-related representations. Our analysis demonstrates that interventions along the identified faithful direction can mitigate hallucinations, while those along the hallucinatory direction can exacerbate them. Building on these insights, we propose Steering LVLMs via SAE Latent Directions (SSL), a plug-and-play method based on SAE-derived latent directions to mitigate hallucinations in LVLMs. Extensive experiments demonstrate that SSL significantly outperforms existing decoding approaches in mitigating hallucinations, while maintaining transferability across different model architectures with negligible additional time overhead. The code is available at https://github.com/huazhenglin2003/SSL.

It has been observed by Belkin et al. that over-parametrized neural networks exhibit a'double descent' phenomenon. That is, as the model complexity (as reflected in the number of features) increases, the test error initially decreases, then increases, and then decreases again. A counterpart of this phenomenon in the time domain has been noted in the context of epoch-wise training, viz., the test error decreases with the number of iterates, then increases, then decreases again. Another anomalous phenomenon is that of grokking wherein two regimes of descent are interrupted by a third regime wherein the mean loss remains almost constant. This note presents a plausible explanation for these and related phenomena by using the theory of two time scale stochastic approximation, applied to the continuous time limit of the gradient dynamics. This gives a novel perspective for an already well studied theme.Key words: stochastic gradient descent; temporal double descent; grokking; overparametrized neural networks; stochastic approximation; singularly perturbed di ff erential equations; two time scales 1. Introduction Many anomalous phenomena regarding the temporal evolution of stochastic gradient descent (SGD) as applied to over-parametrized neural networks have been pointed out in literature. We specifically consider the following: 1. T emporal double descent: Beginning with Belkin et al. [9], the phenomenon of ' double descent ' in the training of over-parametrized neural networks using stochastic gradient descent (SGD) has been flagged and extensively studied from various angles [1, 8, 10, 18, 20, 25, 31, 32, 36, 42].

In practical federated learning (FL), the large communication overhead between clients and the server is often a significant bottleneck. Gradient compression methods can effectively reduce this overhead, while error feedback (EF) restores model accuracy. Moreover, due to device heterogeneity, synchronous FL often suffers from stragglers and inefficiency-issues that asynchronous FL effectively alleviates. However, in asynchronous FL settings-which inherently face three major challenges: asynchronous delay, data heterogeneity, and flexible client participation-the complex interactions among these system/statistical constraints and compression/EF mechanisms remain poorly understood theoretically. In this paper, we fill this gap through a comprehensive convergence study that adequately decouples and unravels these complex interactions across various FL frameworks. We first consider a basic asynchronous FL framework AsynFL, and establish an improved convergence analysis that relies on fewer assumptions and yields a superior convergence rate than prior studies. We then extend our study to a compressed version, AsynFLC, and derive sufficient conditions for its convergence, indicating the nonlinear interaction between asynchronous delay and compression rate. Our analysis further demonstrates how asynchronous delay and data heterogeneity jointly exacerbate compression-induced errors, thereby hindering convergence. Furthermore, we study the convergence of AsynFLC-EF, the framework that further integrates EF. We prove that EF can effectively reduce the variance of gradient estimation under the aforementioned challenges, enabling AsynFLC-EF to match the convergence rate of AsynFL. We also show that the impact of asynchronous delay and flexible participation on EF is limited to slowing down the higher-order convergence term. Experimental results substantiate our analytical findings very well.

This study addresses the problem of hallucinated span detection in the outputs of large language models. It has received less attention than output-level hallucination detection despite its practical importance. Prior work has shown that attentions often exhibit irregular patterns when hallucinations occur. Motivated by these findings, we extract features from the attention matrix that provide complementary views capturing (a) whether certain tokens are influential or ignored, (b) whether attention is biased toward specific subsets, and (c) whether a token is generated referring to a narrow or broad context, in the generation. These features are input to a Transformer-based classifier to conduct sequential labelling to identify hallucinated spans. Experimental results indicate that the proposed method outperforms strong baselines on hallucinated span detection with longer input contexts, such as data-to-text and summarisation tasks.

Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial dictionaries. Data-agnostic analytical dictionaries, such as the discrete Fourier transform, wavelets and graph Fourier, have seen wide adoption due to efficient implementations and good practical performance. On the other hand, dictionaries learned from data offer sparser and more accurate solutions but require learning of both the dictionaries and the coding coefficients. This becomes especially challenging for multi-dictionary scenarios since encoding coefficients correspond to all atom combinations from the dictionaries. To address this challenge, we propose a low-rank coding model for 2-dictionary scenarios and study its data complexity. Namely, we establish a bound on the number of samples needed to learn dictionaries that generalize to unseen samples from the same distribution. We propose a convex relaxation solution, called AODL, whose exact solution we show also solves the original problem. We then solve this relaxation via alternating optimization between the sparse coding matrices and the learned dictionaries, which we prove to be convergent. We demonstrate its quality for data reconstruction and missing value imputation in both synthetic and real-world datasets. For a fixed reconstruction quality, AODL learns up to 90\% sparser solutions compared to non-low-rank and analytical (fixed) dictionary baselines. In addition, the learned dictionaries reveal interpretable insights into patterns present within the samples used for training.

Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in such settings but methods like Local Stochastic Gradient Descent (Local SGD) show great promise in reducing this additional communication overhead. Local SGD consists of three parts: a local optimization process, an aggregation mechanism, and an outer optimizer that uses the aggregated updates from the nodes to produce a new model. While there exists an extensive literature on understanding the impact of hyperparameters in the local optimization process, the choice of outer optimizer and its hyperparameters is less clear. We study the role of the outer optimizer in Local SGD, and prove new convergence guarantees for the algorithm. In particular, we show that tuning the outer learning rate allows us to (a) trade off between optimization error and stochastic gradient noise variance, and (b) make up for ill-tuning of the inner learning rate. Our theory suggests that the outer learning rate should sometimes be set to values greater than $1$. We extend our results to settings where we use momentum in the outer optimizer, and we show a similar role for the momentum-adjusted outer learning rate. We also study acceleration in the outer optimizer and show that it improves the convergence rate as a function of the number of communication rounds, improving upon the convergence rate of prior algorithms that apply acceleration locally. Finally, we also introduce a novel data-dependent analysis of Local SGD that yields further insights on outer learning rate tuning. We conduct comprehensive experiments with standard language models and various outer optimizers to validate our theory.

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of suboptimality called 'gradient discrepancy', and in particular a 'kernel gradient discrepancy' (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel charasterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and prediction-centric uncertainty quantification presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.

Graph Neural Networks (GNNs) are widely used in learning on graph-structured data, yet a principled understanding of why they succeed or fail remains elusive. While prior works have examined architectural limitations such as over-smoothing and over-squashing, these do not explain what enables GNNs to extract meaningful representations or why performance varies drastically between similar architectures. These questions are related to the role of generalisation: the ability of a model to make accurate predictions on unlabelled data. Although several works have derived generalisation error bounds for GNNs, these are typically loose, restricted to a single architecture, and offer limited insight into what governs generalisation in practice. In this work, we take a different approach by deriving the exact generalisation error for GNNs in a transductive fixed-design setting through the lens of signal processing. From this viewpoint, GNNs can be interpreted as graph filter operators that act on node features via the graph structure. By focusing on linear GNNs while allowing non-linearity in the graph filters, we derive the first exact generalisation error for a broad range of GNNs, including convolutional, PageRank-based, and attention-based models. The exact characterisation of the generalisation error reveals that only the aligned information between node features and graph structure contributes to generalisation. Furthermore, we quantify the effect of homophily on generalisation. Our work provides a framework that explains when and why GNNs can effectively leverage structural and feature information, offering practical guidance for model selection.

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

We propose and study Sparse Polyak, a variant of Polyak's adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such settings, the standard Polyak step size performs poorly, requiring an increasing number of iterations to achieve optimal statistical precision-even when, the problem remains well conditioned and/or the achievable precision itself does not degrade with problem size. We trace this limitation to a mismatch in how smoothness is measured: in high dimensions, it is no longer effective to estimate the Lipschitz smoothness constant. Instead, it is more appropriate to estimate the smoothness restricted to specific directions relevant to the problem (restricted Lipschitz smoothness constant). Sparse Polyak overcomes this issue by modifying the step size to estimate the restricted Lipschitz smoothness constant. We support our approach with both theoretical analysis and numerical experiments, demonstrating its improved performance.