We deploy a simple into our everyday lives as search engines (Jin et al., 2025; statistical framework based on risk control (Angelopoulos Xiong et al., 2024), coding assistants (Zhao et al., 2023), et al., 2022) that converts any safety signal into a binary and companions (Zhang et al., 2025a). As their applicability grows, so does the potential harm caused by malicious decision rule, and offers statistical guarantees on the false LLM outputs. Despite remarkable performance across a alarm or missed detection rate. The framework is universally applicable to different monitoring purposes and can leverage wide range of tasks, LLMs remain prone to generating halarbitrary proxy signals. Through experiments on mathematlucinated, factually incorrect (Ravichander et al., 2025), or ical problem solving and red teaming conversations, we harmful output (Yu et al., 2025) when deployed.

What if a reasoning model could decide when to decompose and parallelize independent subtasks, how many concurrent threads to spawn, and how to coordinate them based on the problem at hand? We provide a detailed analysis of recent progress in the field of parallel reasoning, especially adaptive parallel reasoning. Disclosure: this post is part landscape survey, part perspective on adaptive parallel reasoning. One of the authors (Tony Lian) co-led ThreadWeaver ( Lian et al., 2025), one of the methods discussed below. The authors aim to present each approach on its own terms. Recent progress in LLM reasoning capabilities has been largely driven by inference-time scaling, in addition to data and parameter scaling ( OpenAI et al., 2024; DeepSeek-AI et al., 2025). Models that explicitly output reasoning tokens (through intermediate steps, backtracking, and exploration) now dominate math, coding, and agentic benchmarks.

Traditional variational Kalman filtering with unknown noise statistics suffers from inconsistent process covariance estimation and slow convergence speed, limiting its practical utility. To address these issues, we introduce a surrogate variable representing the process-noise-free state, which enables explicit modeling and inference of process noise statistics. In addition, we reformulate the conventional coordinate ascent variation inference (CAVI) as a marginalized maximum a posteriori problem, followed by a single-step hyperparameter fitting. This reformulation obviates the need for multiple inner iterations inherent to CAVI and decouples the design of the covariance tracking filters. Consequently, this architecture permits the deployment of higher-order filters for covariance tracking and enables sliding-window hyperparameter estimation. Notably, when this window encompasses all historical data, the covariance tracking estimator intrinsically operates as a zero-phase filter. Numerical simulations validate the theoretical framework, demonstrating the enhanced convergence speed and superior estimation accuracy compared with existing methods.

Effective sub-typing (also known as grouping or clustering) of patients using their electronic health record (EHR) data can greatly inform precision medicine efforts. However, subtyping temporal EHR datasets is known to be challenging due to inherent EHR issues, including complexity and irregularity. In this study, we propose a self-supervised Mamba-based model that learns effective EHR representations and enables enhanced patient subtyping. We evaluate the proposed model on public and private real-world EHR datasets to classify the data based on the available labels and subtype patients based on the representations learned from the model. Through an extensive set of experiments, we demonstrate that our model's design choices lead to better performance compared to competitive baseline models for prediction. Moreover, we evaluate several clustering techniques to demonstrate that our findings offer valuable insights into subtyping patients based on temporal records from EHR models\footnote{Our implementations are available at https://github.com/healthylaife/triplet_mamba.

We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets. This result generalizes prior analyses restricted to either stationary (single-task) deep models or continual linear models. We show that global convergence generally fails, even for simple models linear in data but nonlinear in parameters. Nevertheless, by leveraging results from nonconvex projection theory, we identify regularity properties of homogeneous deep networks that guarantee local linear convergence under random and cyclic task sequences. Finally, we extend our analysis to continual regression, unifying the framework for homogeneous models.

Many decoding methods for large language models can be understood as shifting probability mass toward outputs that are more likely under the model, either locally at the token level or globally at the sequence level. Therefore, their success depends on a fundamental question: when does sequence probability, that is, the conditional probability of a continuation given a prompt, actually align with correctness? In this paper, we set out to quantify this relationship across decoding methods, models, and benchmarks at four levels: across decoding methods, across hyperparameters within a method, across prompt-answer pairs within a dataset, and across repeated responses to the same prompt. We find that higher sequence probability is often predictive of correctness across prompt-answer pairs within a fixed dataset. However, this relationship does not generally transfer to decoding decisions: increasing sequence probability by changing hyperparameters or methods does not reliably improve accuracy. Further, sequence probability is not a good indicator of correctness for responses to the same prompt. These findings clarify when decoding can and cannot be expected to improve correctness, and provide practical guidance for decoding, self-consistency, and verifier-free self-improvement.

Modeling and sampling from the underlying distribution of asynchronous event sequences are crucial in various real-world applications, including social networks, medical diagnosis, and financial transactions. Existing autoregressive methods suffer from error accumulation during multi-step generation, while non-autoregressive diffusion methods are typically limited to fixed-length output sequences. In this paper, we propose Latent Block-Diffusion Temporal Point Processes (LBDTPP), a novel semi-autoregressive TPP framework that introduces a latent block diffusion mechanism for high-quality and variable-length event sequence generation. The core idea is to define an autoregressive probability distribution over event blocks in latent space and perform Gaussian diffusion within each block. By sequentially generating blocks while simultaneously sampling events in each block, LBDTPP preserves the length flexibility of autoregressive TPPs and inherits the parallel high-quality generation capability of diffusion models. Theoretically, we derive Wasserstein error bounds showing that, under suitable local approximation and prefix-stability assumptions, block-wise generation can reduce error accumulation compared with event-wise autoregressive generation. Extensive experiments on six real-world benchmark datasets demonstrate that LBDTPP outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks. Further empirical analyses verify the benefits of latent-space diffusion and block-wise generation, and reveal the trade-off between generation quality and block size. Our code is available at https://github.com/Zh-Shuai/LBDTPP.

State-space models provide a powerful framework for describing the evolution of hidden states in dynamical systems [3], [4], [1]. Conventionally, state-space models assume Gaussian measurement and state noise, owing to their tractability and well-characterized statistical properties. However, many real-world phenomena are subject to perturbations that deviate from the conventional Gaussian noise assumption. In radio interferometry, for instance, observational data are frequently corrupted by non-Gaussian noise sources such as radio-frequency interference (RFI) [5], [2], which originates from man-made signals and introduces significant distortions into astronomical measurements [6], [30]. Such interference produces sporadic high-power spikes in the measured visibilities, leading to heavy-tailed statistics. Many radio-interferometric reconstruction methods assume Gaussian additive noise [7], [31], [33], [35], an approximation that can lead to inaccurate reconstructions when the heavy-tailed nature of real-world measurement noise is not properly accounted for. In the realm of state-space modeling, addressing non-Gaussian noise has led to the development of various methodological approaches, notably particle filtering and non-conventional Kalman filters. Particle filters [8], or Sequential Monte Carlo methods, are designed to handle non-linear and non-Gaussian state-space models by representing the posterior distribution with a set of weighted samples [9], [10], [32].

Attention mechanisms have demonstrated remarkable empirical success in identifying relevant information from large collections of tokens, yet the theoretical principles underlying this behavior remain poorly understood. We study a stylized softmax-attention model in which a query vector is learned by stochastic gradient ascent from a collection of informative and nuisance tokens. Exploiting the symmetry of the model, we derive a population objective and characterize the limiting ordinary differential equation governing the learning dynamics. Using tools from stochastic approximation and dynamical systems theory, we establish a rigorous connection between the stochastic learning algorithm and its deterministic limit. Our main result shows that, under suitable high-dimensional scaling assumptions and standard step-size conditions, the learned query converges almost surely to the one-dimensional signal subspace spanned by the latent informative direction. Equivalently, the query asymptotically recovers the latent signal up to the intrinsic sign ambiguity. These results provide a rigorous theoretical foundation for understanding attention mechanisms as signal extraction procedures in high-dimensional noisy environments and offer a dynamical-systems perspective on how attention discovers relevant information in the presence of substantial noise.

Deep neural networks using state space models as layers are well suited for longrange sequence tasks but can be challenging to compress after training. We use that regularizing the sum of Hankel singular values of state space models leads to a fast decay of these singular values and thus to compressible models. To make the proposed Hankel singular value regularization scalable, we develop an algorithm to efficiently compute the Hankel singular values during training iterations by exploiting the specific block-diagonal structure of the system matrices that we use in our state space model parametrization. Experiments on Long Range Arena benchmarks demonstrate that the regularized state space layers are up to 10 more compressible than standard state space layers while maintaining high accuracy.