Rethinking the Personalized Relaxed Initialization in the Federated Learning: Consistency and Generalization

Federated learning (FL) is a distributed paradigm that coordinates massive local clients to collaboratively train a global model via stage-wise local training processes on the heterogeneous dataset. Previous works have implicitly studied that FL suffers from the ``client-drift'' problem, which is caused by the inconsistent optimum across local clients. However, till now it still lacks solid theoretical analysis to explain the impact of this local inconsistency. To alleviate the negative impact of ``client drift'' and explore its substance in FL, in this paper, we first propose an efficient FL algorithm FedInit, which allows employing the personalized relaxed initialization state at the beginning of each local training stage. Specifically, FedInit initializes the local state by moving away from the current global state towards the reverse direction of the latest local state. Moreover, to further understand how inconsistency disrupts performance in FL, we introduce the excess risk analysis and study the divergence term to investigate the test error in FL. Our studies show that optimization error is not sensitive to this local inconsistency, while it mainly affects the generalization error bound. Extensive experiments are conducted to validate its efficiency. The proposed FedInit method could achieve comparable results compared to several advanced benchmarks without any additional training or communication costs. Meanwhile, the stage-wise personalized relaxed initialization could also be incorporated into several current advanced algorithms to achieve higher generalization performance in the FL paradigm.

VAN-AD: Visual Masked Autoencoder with Normalizing Flow For Time Series Anomaly Detection

Time series anomaly detection (TSAD) is essential for maintaining the reliability and security of IoT-enabled service systems. Existing methods require training one specific model for each dataset, which exhibits limited generalization capability across different target datasets, hindering anomaly detection performance in various scenarios with scarce training data. To address this limitation, foundation models have emerged as a promising direction. However, existing approaches either repurpose large language models (LLMs) or construct largescale time series datasets to develop general anomaly detection foundation models, and still face challenges caused by severe cross-modal gaps or in-domain heterogeneity. In this paper, we investigate the applicability of large-scale vision models to TSAD. Specifically, we adapt a visual Masked Autoencoder (MAE) pretrained on ImageNet to the TSAD task. However, directly transferring MAE to TSAD introduces two key challenges: overgeneralization and limited local perception. To address these challenges, we propose VAN-AD, a novel MAE-based framework for TSAD. To alleviate the over-generalization issue, we design an Adaptive Distribution Mapping Module (ADMM), which maps the reconstruction results before and after MAE into a unified statistical space to amplify discrepancies caused by abnormal patterns. To overcome the limitation of local perception, we further develop a Normalizing Flow Module (NFM), which combines MAE with normalizing flow to estimate the probability density of the current window under the global distribution. Extensive experiments on nine real-world datasets demonstrate that VAN-AD consistently outperforms existing state-of-the-art methods across multiple evaluation metrics.We make our code and datasets available at https://github.com/PenyChen/VAN-AD.

Kronecker-Structured Nonparametric Spatiotemporal Point Processes

Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges. Classical Poisson and Hawkes processes rely on restrictive parametric assumptions that limit their ability to capture complex interaction patterns, while recent neural point process models increase representational capacity but integrate event information in a black-box manner, hindering interpretable relationship discovery. To address these limitations, we propose a Kronecker-Structured Nonparametric Spatiotemporal Point Process (KSTPP) that enables transparent event-wise relationship discovery while retaining high modeling flexibility. We model the background intensity with a spatial Gaussian process (GP) and the influence kernel as a spatiotemporal GP, allowing rich interaction patterns including excitation, inhibition, neutrality, and time-varying effects. To enable scalable training and prediction, we adopt separable product kernels and represent the GPs on structured grids, inducing Kronecker-structured covariance matrices. Exploiting Kronecker algebra substantially reduces computational cost and allows the model to scale to large event collections. In addition, we develop a tensor-product Gauss-Legendre quadrature scheme to efficiently evaluate intractable likelihood integrals. Extensive experiments demonstrate the effectiveness of our framework.

Reasoning over Semantic IDs Enhances Generative Recommendation

Recent advances in generative recommendation have leveraged pretrained LLMs by formulating sequential recommendation as autoregressive generation over a unified token space comprising language tokens and itemic identifiers, where each item is represented by a compact sequence of discrete tokens, namely Semantic IDs (SIDs). This SID-based formulation enables efficient decoding over large-scale item corpora and provides a natural interface for LLM-based recommenders to leverage rich world knowledge. Meanwhile, breakthroughs in LLM reasoning motivate reasoning-enhanced recommendation, yet effective reasoning over SIDs remains underexplored and challenging. Itemic tokens are not natively meaningful to LLMs; moreover, recommendation-oriented SID reasoning is hard to evaluate, making high-quality supervision scarce. To address these challenges, we propose SIDReasoner, a two-stage framework that elicits reasoning over SIDs by strengthening SID--language alignment to unlock transferable LLM reasoning, rather than relying on large amounts of recommendation-specific reasoning traces. Concretely, SIDReasoner first enhances SID-language alignment via multi-task training on an enriched SID-centered corpus synthesized by a stronger teacher model, grounding itemic tokens in diverse semantic and behavioral contexts. Building on this enhanced alignment, SIDReasoner further improves recommendation reasoning through outcome-driven reinforced optimization, which guides the model toward effective reasoning trajectories without requiring explicit reasoning annotations. Extensive experiments on three real-world datasets demonstrate the effectiveness of our reasoning-augmented SID-based generative recommendation. Beyond accuracy, the results highlight the broader potential of large reasoning models for generative recommendation, including improved interpretability and cross-domain generalization.

Multinoulli Extension: A Lossless Continuous Relaxation for Partition-Constrained Subset Selection

Identifying the most representative subset for a close-to-submodular objective while satisfying the predefined partition constraint is a fundamental task with numerous applications in machine learning. However, the existing distorted local-search methods are often hindered by their prohibitive query complexities and the rigid requirement for prior knowledge of difficult-to-obtain structural parameters. To overcome these limitations, we introduce a novel algorithm titled Multinoulli-SCG, which not only is parameter-free, but also can achieve the same approximation guarantees as the distorted local-search methods with significantly fewer function evaluations. More specifically, when the objective function is monotone $α$-weakly DR-submodular or $(γ,β)$-weakly submodular, our Multinoulli-SCG algorithm can attain a value of $(1-e^{-α})\text{OPT}-ε$ or $(\frac{γ^{2}(1-e^{-(β(1-γ)+γ^2)})}{β(1-γ)+γ^2})\text{OPT}-ε$ with only $O(1/ε^{2})$ function evaluations, where OPT denotes the optimal value. The cornerstone of our Multinoulli-SCG algorithm is an innovative continuous-relaxation framework named Multinoulli Extension(ME), which can effectively convert the discrete subset selection problem subject to partition constraints into a solvable continuous maximization focused on learning the optimal multinoulli priors across the concerned partition. In sharp contrast with the well-established multi-linear extension for submodular subset selection, a notable advantage of our proposed ME is its intrinsic capacity to provide a lossless rounding scheme for any set function. Furthermore, based on our proposed ME, we also present two novel online algorithms, namely, Multinoulli-OSCG and Multinoulli-OSGA, for the unexplored online subset selection problems over partition constraints.

Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs

Push-Sum-based decentralized learning enables optimization over directed communication networks, where information exchange may be asymmetric. While convergence properties of such methods are well understood, their finite-iteration stability and generalization behavior remain unclear due to structural bias induced by column-stochastic mixing and asymmetric error propagation. In this work, we develop a unified uniform-stability framework for the Stochastic Gradient Push (SGP) algorithm that captures the effect of directed topology. A key technical ingredient is an imbalance-aware consistency bound for Push-Sum, which controls consensus deviation through two quantities: the stationary distribution imbalance parameter $δ$ and the spectral gap $(1-λ)$ governing mixing speed. This decomposition enables us to disentangle statistical effects from topology-induced bias. We establish finite-iteration stability and optimization guarantees for both convex objectives and non-convex objectives satisfying the Polyak--Łojasiewicz condition. For convex problems, SGP attains excess generalization error of order $\tilde{\mathcal{O}}\!\left(\frac{1}{\sqrt{mn}}+\fracγ{δ(1-λ)}+γ\right)$ under step-size schedules, and we characterize the corresponding optimal early stopping time that minimizes this bound. For PŁ objectives, we obtain convex-like optimization and generalization rates with dominant dependence proportional to $κ\!\left(1+\frac{1}{δ(1-λ)}\right)$, revealing a multiplicative coupling between problem conditioning and directed communication topology. Our analysis clarifies when Push-Sum correction is necessary compared with standard decentralized SGD and quantifies how imbalance and mixing jointly shape the best attainable learning performance.

Statistical Early Stopping for Reasoning Models

While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically principled early stopping methods that monitor uncertainty signals during generation to mitigate this issue. Our first approach is parametric: it models inter-arrival times of uncertainty keywords as a renewal process and applies sequential testing for stopping. Our second approach is nonparametric and provides finite-sample guarantees on the probability of halting too early on well-posed queries. We conduct empirical evaluations on reasoning tasks across several domains and models. Our results indicate that uncertainty-aware early stopping can improve both efficiency and reliability in LLM reasoning, and we observe especially significant gains for math reasoning.

ZeroS: Zero-Sum Linear Attention for Efficient Transformers

Linear attention methods offer Transformers $O(N)$ complexity but typically underperform standard softmax attention. We identify two fundamental limitations affecting these approaches: the restriction to convex combinations that only permits additive information blending, and uniform accumulated weight bias that dilutes attention in long contexts. We propose Zero-Sum Linear Attention (ZeroS), which addresses these limitations by removing the constant zero-order term $1/t$ and reweighting the remaining zero-sum softmax residuals. This modification creates mathematically stable weights, enabling both positive and negative values and allowing a single attention layer to perform contrastive operations. While maintaining $O(N)$ complexity, ZeroS theoretically expands the set of representable functions compared to convex combinations. Empirically, it matches or exceeds standard softmax attention across various sequence modeling benchmarks.

A Study of Adaptive Modeling Towards Robust Generalization

Large language models (LLMs) increasingly support reasoning over biomolecular structures, but most existing approaches remain modality-specific and rely on either sequence-style encodings or fixed-length connector tokens for structural inputs. These designs can under-expose explicit geometric cues and impose rigid fusion bottlenecks, leading to over-compression and poor token allocation as structural complexity grows. We present a unified all-atom framework that grounds language reasoning in geometric information while adaptively scaling structural tokens. The method first constructs variable-size structural patches on molecular graphs using an instruction-conditioned gating policy, enabling complexity-aware allocation of query tokens. It then refines the resulting patch tokens via cross-attention with modality embeddings and injects geometry-informed tokens into the language model to improve structure grounding and reduce structural hallucinations. Across diverse all-atom benchmarks, the proposed approach yields consistent gains in heterogeneous structure-grounded reasoning. An anonymized implementation is provided in the supplementary material.

Scaling-Aware Adapter for Structure-Grounded LLM Reasoning

Large language models (LLMs) are enabling reasoning over biomolecular structures, yet existing methods remain modality-specific and typically compress structural inputs through sequence-based tokenization or fixed-length query connectors. Such architectures either omit the geometric groundings requisite for mitigating structural hallucinations or impose inflexible modality fusion bottlenecks that concurrently over-compress and suboptimally allocate structural tokens, thereby impeding the realization of generalized all-atom reasoning. We introduce Cuttlefish, a unified all-atom LLM that grounds language reasoning in geometric cues while scaling modality tokens with structural complexity. First, Scaling-Aware Patching leverages an instruction-conditioned gating mechanism to generate variable-size patches over structural graphs, adaptively scaling the query token budget with structural complexity to mitigate fixed-length connector bottlenecks. Second, Geometry Grounding Adapter refines these adaptive tokens via cross-attention to modality embeddings and injects the resulting modality tokens into the LLM, exposing explicit geometric cues to reduce structural hallucination. Experiments across diverse all-atom benchmarks demonstrate that Cuttlefish achieves superior performance in heterogeneous structure-grounded reasoning. Code is available at the project repository.